Macroeconomic models with financial frictions and insurance cycles.

Summary Some insurance markets are subject to the well-known phenomenon of "underwriting cycles," consisting of a stress phase in which premiums and profits increase while capacity decreases, followed by a slack phase characterized by falling prices and the rebuilding of capacity. These cycles are difficult to explain in the classical framework of perfect financial markets. They imply a certain predictability of premiums, a correlation between insurers' ROE (return on equity) and claims, which seems to contradict the principle of no arbitrage opportunities. We show that these properties can be perfectly explained in a competitive equilibrium model with financial frictions. Our model extends the classical ruin theory approach to a macroeconomic model where insurance premiums are endogenous and result from the equilibrium between supply and demand of contracts. Companies determine their underwriting and share issuance or redemption policies in order to maximize their market value. Insurance premiums are a deterministic function of the total market capitalization of insurers. Our results explain why insurance premiums are predictable and the correlation betweenROEand claims. In fact, rather than true cycles, premiums and capacities oscillate between two extreme values with reversals when one of these values is reached.Our model illustrates the power of the new generation of macroeconomic models with financial frictions, initiated by Brunnermeier and Sannikov (2014), that can be successfully applied to the analysis of other issues important for insurance and reinsurance markets.